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Fljaire 2. I*lmi of Tower Clock for I'niver^^Hv .if Chlciiyo, 



The Tower Clock 



and 



How to Make It 



A Practical and Theoretical Treatise on the Construction 

of a Chiming Tower Clock, vi/itb Full Working 

Drawings Photographed to Scale. 



By E. B. Person, A. M., Mass. 

Instructor lii drawing and machine design in The Chicago Maiujiil 
Training School of The University of Chicago. 



CHICAGO: 
Hazlitt S( Walker, Publishers 
1903. 






6 



THE. LIBRARY OF 
CONGRESS, 

Two Copies Received 

MAY 29 1903 

Copyiight tntty 
CLASSV ^ XXo. No. 

COPY a. 



Copyright, 1903, 

by 

Hazlitt & Walker. 



PREFACE. 

A number of volumes might be written on the subject of 
clocks and bells, and their history. The subject matter is 
very interesting reading; but this is not a history of clock 
making. It is only a description of a clock which has been 
built for the University of Chicago by pupils of the Chicago 
Manual Training School, Boys ranging from 14 to 18 years 
of age. The theoretical and time calculations were made 
by the instructor; but the drawings, patterns and machine 
work are the work of the boys. The assembled drawings 
of the clock shown in Figs, i and 2, are the personal work 
of the whole Senior class of about 45 pupils, each one of 
whom had a particular part assigned to him ; and after that 
part had been drawn in detail, it was put in its proper place 
in these drawings by the pupil who had made it, so that the 
assembled drawings are the composite work of the class. 

A part of our course in drawing and machine design is 

the designing and building of some machine, and this clock 

is one in a list of machines which includes steam engines 

from six to ten horse power, a heavy drill press, a steam 

hammer, a cutter grinder and numerous other machine tools 

for the shops. 

E. B.'Ferson 



SPECIFICATIONS OF THE CLOCK. 

The clock was designed from a purely mechanical stand- 
point and without any preconceived or sentimental ideas, 
but simply as a machine to keep time, the object being to do 
the work accurately with the least possible number of parts 
and those parts of the simplest form. For the reasons above 
stated it was decided to build the clock as three separate 
machines to be mounted on a common bed-plate. 

First, a time part, which should furnish power to drive 
the visible time-keepers; i. e., the hands on the dials. 

Second, a striking part, to give the time on the hour bell, 
and third, a chime part to give the musical quarters on four 
smaller bells. This arrangement of parts is a decided ad- 
vantage, for in case anything should happen to any one of 
the parts, that part may be disconnected, and the necessary 
repairs made without any interference with the other parts. 

Perhaps the quickest way to get to our subject would be 
to follow the preacher's method and give you a text, which 
in this case would be the specifications for the clock. They 
are as follows : 

1. To make and set a clock with four dials of 12 feet 
diameter, striking the hours and Westminster quarters on 
bells which would be the second, third, fourth, seventh and 
tenor of a peal of eight, the tenor to weigh 7,000 pounds. 

2. The dials to be illuminated, with the figures and min- 
utes of cast-iron in rings ; the body of the dial to be of opal 
glass of 22 ounces per square foot. There must be no 
straiuht radial bars from the center. There must be a clear 

(5) 



THE TOWER CLOCK 



opening in the wall the full diameter of the dial, and no 
ledge upon which snow or ice can collect. 

3. The minute hands to have a short external counter- 
poise, painted the same color as the dial ; the hands, figures 
and minutes tO' be black, and the framework of the dial gilt. 

4. The escapement to be a Sir Edmund Beckett's double 
three-legged gravity, 

5. The pendulum to have a cast-iron jar with steel tube; 
mercury compensation ; to beat seconds and swing two and 
one-half degrees from o or a total arc of five degrees. 

6. The clock to rest on steel I-beams entirely independ- 
ent of the floor of the clock room. The pendulum cock to 
rise from the clock frame. 

7. There must be a minute dial, and a dial for seconds. 

8. The time part to have an independent maintaining 
power to keep it in motion while being wound, and to be so 

designed that it will run eight days. 

9. The striking parts to be wound up every day. The 
fourth quarter bell to have two hammers. 

10. The striking of the hours to let off independently of 
the quarters, and the first blow of the hour struck exactly 
on the hour; the other quarters to begin exactly a*- 15, 30 
and 45 minutes. 

11. The hour hammer to be not less than one-sixtieth 
of the weight of the bell, and be raised not less than nine 
inches ; the quarters' hammers to increase in weight from 
a sixtieth to a fortieth of the weight of their bells. 

The small hammers to be raised not less than six inches. 



HOW TO MAKE IT. 7 

12. . The large going wheels and the larger pinions to be 
cast-iron, the small pinions of steel, and all bushings of 
brass. 

13. The winding barrels to be of cast-iron of sufificient 
thickness to withstand the compression caused by the rope 
in winding ; the rope used to be a one- fourth inch steel rope, 
which must not be wound more than one layer on the wheel. 

14. The flies to be at the back of the clock, and long 
enough to make the intervals between strokes uniform and 

sufficiently great. 

15. All the metal except working surfaces to be painted 
University maroon. 

16. There must be something to warn or stop the wind- 
ing; and also a box about three feet deep filled with small 
stone to catch the weights if they fall. 

17. All shafts to be made to take out separately by un- 
screwing the bushings. 

18. The clock to be enclosed in a room as near air-tight 
as possible, to keep out dust and avoid sudden changes of 
temperature. 



THE TIME TRAIN. 

For the time train a quarter inch wire rope on the barrel, 
four turns in each 24 hours, for eight days, gives a barrel, 
No. I, eight inches long; and with two extra turns for care- 
less winding makes it eight and one-half inches long, which 
is a convenient length. On the shaft with this goes the 
great wheel. No. 2, of 120 teeth, which will turn once in 
six hours ; this must not be keyed to the going shaft, but 
is to be driven bv ratchet teeth on one end of the barrel and 
a pawl attached to one of the arms of the great wheel. The 
winding wheel. No. 4, and the drum, are keyed to the going 
shaft. 

The winding pinion. No. 3, is on a shaft, the end of which 
is squared to fit the key ; this pinion is made to slide on a 
feather key in the shaft, so that it can be thrown out of gear 
when not winding:. 



'&• 



The maintaining power. Fig. 3, consists of a shaft. A, a 
straight lever, B, a segment of a pinion, C, a curved, double 
lever, D, a weight E. The shaft. A, slides endwise to en- 
gage the teeth of the pinion segment with the teeth of the 
great wheel. No. 2, the straight lever has a handle at both 
ends to assist in throwing the pinion out or in and a shield 
at the outer end to cover the end of the winding shaft, No. 
3, when the key is not on it. 

The curved lever is dduble, and (he pinion segment turns 
loosely between the halves, and on the shaft, A ; it is held 
up in its place by a light spring, F ; the weight, E, is also 
held between the two halves of the double lever. 



HOW TO MAKE IT. 



The action is as follows : The end of the lever, B, covers 
the end of the winding shaft so that it is necessary to raise 
it before putting the key on the winding shaft; it is raised 




till it strikes a stop, and then i)ushc(l in till the pinion seg- 
ment engages with the going wheel of the train, when the 
weight, E, acting through the levers, furnishes power to 
drive the clock-train while the going weight is being wound 



lO THE TOWER CLOCK 

up. Of course the weight on the maintaining power must 
be so proportioned to the leverage that it will be equal to 
the power of the going barrel and its weight, a simple prop- 
osition in mechanics. 

The number of teeth on the pinion segment, C, is sufficient 
to maintain power for fifteen minutes, at the end of which 
time the lever, B, will come down and again cover the end 
of the winding shaft ; or, it may be pumped out of gear 
and dropped down. In case it is forgotten, the spring, F, 
will allow the segment 'to pass out of gear of itself and will 
simply allow it to give a click as it slips over each tooth in 
the going wheel ; if this were not provided for, it would 
stop the clock. As before stated, the great or going wheel 
has 120 teeth and turns once in six hours. The second shaft 
in the train, being the hour shaft, the pinion, No. 6 must 
have 20 teeth. On the hour shaft, No. 5 are : 

First, the dial gears and a dial with the minute and hour 
hands, to set the clock by. This, of course, has the usual 
gears of 45 teeth in the wheel and 15 teeth in the pinion, 
and 48 teeth in the wheel, and 12 teeth in the pinion in order 
to change the speed so as to give the minutes and hours on 
the setting dial. See Fig. i-A, which shows the detail of the 
setting-dial. The shaft. A, is the hour shaft. The bushing, 
B, with its studs, a, b, c, supports the dial, C, and carries the 
change gears, E, F, G, H. The shaft extension, D, is 
screwed to the end of the shaft, A, by the screw, D\ form- 
ing the arbor for the minute hand. The minute hand is 
held in place on its arbor by the head of the screw, D^. The 
arbor, D, also carries the pinion, E, of fifteen teeth, driving 
the wheel, F, of forty-five teeth, which is carried on the 
stud, c, being moimted on the hub of the pinion, G, of 
twelve teeth, which, in turn, drives the wheel of forty-eight 
teeth whose hub forms the arbor for the hour hand, revolv- 
ing once in twelve hours. 



HOW TO MAKE IT. 



I I 



Second, a pair of bevel gears, No. 7 (for leading oflf 
bevels to tbe large dials), of 44 and 48 teeth respectively, of 
which we shall say more later on. 

Third, the second wheel in the train, of 105 teeth. No. 8. 
The hub of this wheel revolves on a steel bushing, E, shown 




Fitj. la. Details of Dial and Motion Work on Clock. 



in Fig. 4, which is keyed to the shaft. On one side of the 
rim of the wheel, A, are cut 60 grooves or teeth, one for each 
minute, to use in setting the hands on the large dials to one 
minute ; the space, B, is 6 degrees, and the set screws, C and 
CS make the lever, D, adjustable to seconds for the finer 
setting of the minute hands, so that they will correspond 
exactly to the striking parts. The set screws which control 
the lever, D, have 20 threads per inch ; the angular move- 
ment for one minute at the center of the screws, C and C^, 
is equal to .1875 inches; one second angular movement 
therefore equals .003125 inches. One revolution of the 



HOW TO MAKE IT. 



screw equals .05 inches ; therefore, one second angular 
movement calls for one-sixteenth revolution of a screw of 20 
threads, and the heads of the screws, C and C^ are for that 
reason divided on their edges into 16 parts. 

In Fig. 4, the wheel, A, which is shown as heing" mounted 
upon the sleeve of the hub, E, should be carried on the 
sleeve of the pinion. No. 6, Figs, i and 2, so that when set- 
ting the hands on the dials, the time train will not be inter- 
fered with in its movement. The arrangement above de- 
scribed takes the place of the friction-tight center arbor in 
a watch or smaller clock, as b> pressing down on the lever, 
F, until the teeth on the side of wheel, A, Fig. 4, (or wheel 
8 of the time train), are disengaged the hour shaft may 
then be rotated independently of the time train. This is 
done when setting the clock roughly while the finer adjust- 
ments are made by the adjusting screws C and C. 

To put this in plain figures: .1875 divided by .05 equals 
3.75 revolutions. Sixty divided by 3.75 equals 16, or one- 
sixteenth revolution. 

Fourth, the dropping wheel, No. 9, or cam, with a pin, No. 
II, on one side of it, for the usual warning before the strike. 
The final drop is done upon the proper second by the cam, 
or -snail, j, on the wheel, No. 10. which revolves once in 15 
minutes. On the other side of the wheel. No. 9, are four 
pins, 2}, a-, 2?, a*, which give the warning of the quarters, 
and on the face of the wheel. No. 9, are four cams, V-, f^, 
f^, f*, which drop at their proper intervals. See Fig. 14. 
On the third shaft are : 

First, the driving pinion. No. 11, of 14 teeth, giving seven 
and "one-half revolutions of this shaft per hour, or eight 
minutes for one revolution. 

Second, the third wheel. No. 13, of 120 teeth. 

Third, a wheel, No. 12, of 48 teeth, driving one of 90 
teeth, No. 10, on a shaft above, giving one revolution in 15 
minutes. A cam, J, Fig. 11, on the side of this wheel gives 
the final drop of the hour striking lever. 



THE TOWER CLOCK 




HOW TO MAKE IT. 1 5 

On the fourth shaft are: 

first, The driven pinion, No. 14, of 15 teeth, giving one 
revokition per minute, and to the end of this shaft is affixed 
a hand to mark seconds on a dial which is made upon the 
bushing of the shaft ; this dial is divided to read seconds. 

Second, The fourth wheel, No. 15, of 120 teeth. 

The fifth shaft is the escapement shaft with its pinion. No. 
16, of 12 teeth, giving one revolution in six seconds. 

I'here is upon this shaft the escapement fly, Fig. 6, with 
vanes or fans as long as it is possible to make them ; length 
is more important than width in any mechanism of this kind, 
as it is the length of the leverage, rather than the surface 
exposed to the pressure of the air, which equalizes the mo- 
tion and softens the blow of the legs of the escapement on 
the pallets. This shaft is short, as all the parts must be 
small, and the shaft would not be stiff enough to stand all 
the strains put upon it, if it was made of the same length as 
the others. 

The escapement is the double three-legged, gravity es- 
capement, invented by Sir Edmund Beckett, the eminent 
English authority on clock design, and designer of the great 
Westminster clock in London, whose general specifications 
I have followed in the design of this clock. 

Referring to Fig. 5, this escapement is so called because 
it has two three-legged wheels, A, B, C, and a, b, c, which 
are placed in diiTerent planes, with a set of three lifting 
pins, D, between them. 

The two wheels must be squared upon the arbor, so that 
there will be no possibility of slipping. They are made 
from heavy sheet steel, with the ends of the arms hardened. 
The lifting pins, D, are shouldered between them, like a 
three-toothed lantern pinion. 

Referring to the enlarged detail in the lower right-hand 
comer of Fig. 5, the shaded portion shows the form which 
has been decided upon for the pinion, D. The pinion is 
made solid on the shaft, J. The wheel. A, B, C, is made to 



i6 



1 HE TOWER. CLOCK 




irOW TO MAKE IT. 1 7 

pass over the pinion, D, and is fitted to a triangular seating 
the size of the circumscribed triangle of the leaves, D, and 
against a collar on the shaft. The wheel a, b, c, is fitted to 
the inscribed triangle of the pinion so that the leaves, D, 
form the shoulders against which it fits. 

The pallets, E and E', also lie in one plane between the 
wheels, but one stop, F, points forward to receive the A, B, 
C, teeth and the other, G, backward to receive the a, b, c, 
teeth, alternately. 

The reason for having two wheels is that with one three- 
legged wheel the pallets could not be far from upright, 
which would require more dead weight to be moved at 
every beat in order to have weight enough to give an eflfec- 
tive impulse to the pendulum. 

There is no particular mechanical advantage jn the two 
wheels being set with the alternate teeth equidistant, ap- 
pearing like a six-legged wheel. They may be set 90 de- 
grees and 30 degrees to the other set, or at any other angle 
in order to get a greater inclination of the pallets, if desired. 
However, the equidistant arrangement is the natural one. 
I need hardly say that a pair of wheels of this kind is very 
different from a six-legged wheel, which would move only 
30 degrees at each beat, while this moves 60 degrees. There 
are also other differences. 

The distance of the pendulum top, H, or cheeks, from 
the center of the 'scape wheel, J, equals the diameter of the 
'scape wheel. 

The lifting pins, D, should not be farther from the center 
than a thirtieth of this distance; otherwise the pallets, E 
and E', will have to be inconveniently thin and light. The 
pins should be so placed that the one which is holding up a 
pallet and the one which is to lift next, will be vertically 
over each other, the third being on a level with the center; 
i. e., they lie in the radii which form the acting faces of 
the teeth of one of the wheels. Fig. 5. 



i8 



THE TOWER CLOCK 



I'hc fly must be as large as possible, and have a large 
roller for the spring to act upon. In the University clock 
the spring clutch- is shown by Fig. 6. 




Fig.e, 



The pallet tails, c e', may be bent for the adjustment of 
the beat. 

The beat pins, c', e'2, are tapped into the ends of the pal- 
let tails. One of them should be threaded left hand, and 
each has a lock nut on the back. The outer ends of the 
pins, where they rest on the pendulum rod, are of ivory, to 
lessen the chatter ; and the one thing which makes a dis- 
tinction between a gravity and a dead-beat escapement must 
be avoided, viz. : the beat pins in the gravity escapement 
must on no account be touched with oil or other grease of 



HOW TO MAKE IT. 



19 



¥iir 





20 THE TOWER CLOCK 

any kind, but left absolutely dry, wbatever they are made of, 
because the slightest adhesion between the beat pins and 
the ijenduluni rod is fatal to the whole action of the escape- 
ment. Care must also be taken that one pallet begins to 
lift simultaneously with the resting of the other, neither 
before nor after. 

The stops on the pallet arms are of steel and are made as 
hard as possible, or it would be still better if they were made 
of agate or other jewels. These stops may have the slight- 
est touch of oil of the best quality, but all surplus must be 
wiped off. 

The distance of the lifting pins, D, from the center, J, 
should not be more than a fortieth of J, H, or the angle of 
impulse will be too great to be convenient. It is difficult 
to make the pallets light enough ; the larger the angle of 
impulse the lighter they must be. 

The length of the pallet tails down to the beat pins is a 
matter of design and appearance, but the action is better 
with long than with short tails. The length shown in the 
drawing looks neat, as the two parts are reciprocally par- 
allel, and it is customary to make them in that way. 

The pins, D, are placed so that the lifting will take place 
equally across the line of centers, K, L, as it is then done 
with the least friction. 

Any gravity escapement requires a heavier weight on the 
going parts than a dead escapement, because it must be 
strong enough to be sure of lifting the pallets quickly and 
firmly; but with this form of escapement the superfluous 
force does not work the pendulum, and it therefore does 
no harm, if the train is good enough not to waste power in 
getting over rough places left in cutting the teeth of the 
wheels. For this reason a high-numbered train is better 
than a low-numbered one, as these defects are greater on 
the larger teeth of a low-numbered train ; and any defect in 
this matter will show itself, or rather, make itself heard. 

In the gravity escapement, the wheel must have a little 



HOW TO MAKE IT. 2t 

run at the pallets before it begins to lift them, and in order 
to do this there ought to be two banking pins, M M', for the 
pallet arms to rest on, just clear of the lifting pins. 

The 'scape wheel should be as light as possible, for every 
blow that is heard in a machine means a loss of power and 
wear of parts; of course, in an escapement, a sudden stop, 
and therefore a blow of some amount, is expected, but the 
light wheel will reduce it to a minimum. 

To bring the time train down to plain figures it stands 
thus: Great wheel, one revolution in six hours, 120 teeth, 
with a pinion of 20 teeth ; hour shaft, 105 teeth, with a pin- 
ion of 14 teeth; seven and one-half minute shaft 120 teeth, 
with a pinion of 15 teeth; one minute shaft, 120 teeth, with 
a pinion of 12 teeth, giving the 'scape wheel six seconds. 

The pendulum. Fig. 9, is suspended from the head or 
cock shown in the figure, and supported by the clock frame 
itself, instead of being hung on a wall, since the intention is 
to set the clock in the center of the clock-room, and also 
because the weight, forty pounds, is not too much for the 
clock frame to carry. The head. A, forms a revolving 
thumb-nut, which is divided into sixty parts around the 
circumference of its lower edge, and the regulating screw, 
B, is threaded ten to the inch. A very fine adjustment is 
thus obtained for regulating the time of the pendulum. The 
lower end of the regulating screw, B, holds the end of the 
pendulum spring, E, which is riveted between two pieces 
of steel, C, and a pin, C, is put through them and the end of 
the regulating screw, by which to suspend the pendulum. 

The cheeks or chops are the pieces D, the lower edges of 
which form the theoretical point of suspension of the pendu- 
lum. These pieces must be perfectly square at their lower 
edges, otherwise the center of gravity would describe a 
cylindrical curve. The chops are clamped tightly in place 
by the setscrews, D', after the pendulum has been hung. 

The point of suspension, and therefore the bend of the 
spring, must be exactly opposite the center of the line of 



22 THE TOWER clock 

intersection of the pallet arms, so that there will be no 
friction of the beat pins on the pendulum rod. The lower 
end of the regulating screw is grooved on one side, sliding 
on a pin to prevent its turning and therefore twisting the 
suspension spring when it is raised or lowered. 

The spring is about three inches long between its points 
of suspension, one and three-eighths inches wide, and one- 
sixtieth of an inch thick. Its lower end is riveted between 
two small blocks of steel, F, and suspended from a pin, F', 
in the upper end of the cap, G, of the pendulum rod. 

The tubular steel portion of the pendulum rod is seven- 
eighths of an inch in diameter and one-thirty-second of an 
inch thick. It is enclosed at each end by the solid ends, G 
and L, and is made as nearly air tight as possible, in order 
to assist in the compensation which is necessary, owing to 
changes of temperature and barometer. 

The compensation is made by means of mercury inclosed 
in a cast-iron bob. The mercury, the bob and the rod to- 
gether, weigh forty pounds. The bob of the pendulum is 
a cast-iron jar, K, three inches in diameter inside, one-quar- 
ter inch thick at the sides, and five-sixteenths thick at the 
bottom, with the cap, J, screwed into its upper end. The 
cap, J, forms also the socket for the lower end of the pen- 
dulum rod, H. The rod, L, one-quarter inch in dianieter, 
screws into the cap, J, and its large end at the same time 
forms a plug for the lower end of the pendulum tube, H. 
The pin, J', holds all these parts together. The rod, L, ex- 
tends nearly to the bottom of the jar, and forms a medium 
for the transmission of the changes in temperature from the 
pendulum tube to the mercury. The screw in the cap, J, is 
for filling or emptying the jar. The jar is finished as 
smoothly as possible, outside and inside, and should be 
coated with at least three coats of shellac inside. Of course 
if one was building ;in astronomical clock, i( would be nec- 
essary to boil the mercury in the jar in order to drive off the 
layer of air between the mercury and the walls of the jar, 



HOW TO MAKE IT. 



23 



but with the smooth finish the shellac will give, in addition 
to the good work of the machinist, the amount of air held 
by the jar can be ignored. The cast-iron jar was decided 
upon because it was safer to handle, can be attached more 
firmly to the rod with less multiplication of parts, and also 
on account of the weight as compared with glass, which is 
the only other thing that should be used, the glass requiring 
a greater height of jar for equal weight. 

Ignoring the rod and its parts for the present, and calling 
the jar one-third of the weight of the mercury, we shall find 
that thirty pounds of mercury, at .49 pounds per cubic inch, 
will fill a cylinder which is three inches inside diameter to a 
height of 8.816 inches, after deducting for the mass of the 
rod L, when the temperature of the mercury is 60 degrees 
F, Mercury expands one-tenth in bulk, while cast-iron ex- 
pands .0066 in diameter; so the sectional area increases as 
1.0066", or 1. 01 32 to I, therefore the mercury will rise 
.i-,oi32, or .087; then the mercury in our jar will rise .767 
of an inch in the ordinary changes of temperature, making 
a total height of 9.58 inches to provide for; so the jar was 
made ten inches long. 

As this is a one-second pendulum, the length from the 
point of suspension to the center of gravity, or center of in- 
ertia, of the bob, was found by the common equation for the 
simple pendulum, viz. : 



t =T 



u 



In which t, is one second; T, is 3.1416; 1, is the length; 
and g, is the force of gravity for Chicago. 

The force of gravity depends upon the latitude and the 
elevation above sea level. Barker's Physics, page 105, gives 
the following npproximalo fnnniiln : 

g = 980.6056 — 2. 5028 cosine 2, d — .000003 h. 
980.6056 = value of gravity at lat. 45 degrees. 
d = latitude of Chicago = 41 degrees 50 minutes. 



24 THE TOWER CLOCK 

h = altitude above sea level, of the clock, in centimeters. 
h = 715 X 12 X 2.54. 
h = 21793.20 centimeters. 
Cosine 2d := Cosine 2.x 41 degrees 50 minutes. 

= Cosine 83 degrees 40 minutes. 

- .1103. 

Substituting- figures in the formula gives : 

g. — 980.6056 — 2.5028 X .1103 — .000003 X 21793.20. 
= 980.6056 — .27605 — .06537 
= 980.2642 dynes. 
= force of gravity at the clock. 

g 
Therefore 1 = — centimeters. 

'J'2 

_ 980.2642 
~ 9.8696 

= 99.321 centimeters. 
= 39.099134 inches. 

Which equals the length of the pendulum rod from its point 
of suspension to the center of inertia, or center of gravity, 
on the clock, when it is in a tower 715 feet above sea level, 
or 13 s feet above the mean lake level at Chicago. This is 
the theoretical length of a mathematical pendulum, but of 
course the pendulum rod must be stiff enough to avoid the 
tendency to bend as it receives its impulse from the pallets; 
and as a bob of forty pounds must be of considerable size, 
the actual or effective center of the swinging weight will be 
some small distance below the point given in the formula. 
This point is called the center of oscillation and also the 
center of percussion, and is really the point in the bob where 
a force or blow used to stop the pendulum suddenly would 
do so without jarring the pendulum in any of its parts or 
producing any sidewise pressure at its point of suspension. 
This does not correspond to the center of gravity of the 
mass of the pendulum, which is a fixed point, but is below it. 

Now let us consider some of the forces collected at the 
center of oscillation. 

I — The center of oscillation. If a body oscillate, or 
swing about a fixed horizontal axis or point of suspension 



HOW TO MAKE IT. 25 

not passing through its center of gravity, there is a point in 
the line drawn from the center of gravity perpendicular to 
the horizontal axis whose motion is the same as it would be 
if it were possible to collect the whole mass of the body at 
that point, and the mass allowed to vibrate, oscillate, or 
swing as a pendulum about the fixed horizontal axis, or 
point of suspension. This point is called the center of oscil- 
lation, and is, as before stated, always below the center of 
gravity. See Fig. 19. 

If A be the point of suspension of a body, B, its center of 
mass, or center of gravity ; K equals the length of the radius 
of gyration of the mass with reference to the point of sus- 
pension, A ; then there is, in the same straight line with A, 
B, and on the opposite of B, from A, a point, C, called the 
center of oscillation, which lias the following properties : 

a — A body may be swung upon A, or at C, indifferently, 
and in either case it will oscillate pendulum-wise with equal 
rapidity or in equal time. 

b — The body thus suspended at either A, or C, will oscil- 
late at the same rate as an ideal simple pendulum of the 
length A, C. 

c — This body will, if struck at C, oscillate round A, with- 
out producing any pressure on the point of suspension or 
supporting axis A. 

d — Though the support at A were withdrawn, as, for In- 
stance, if the body were floating submerged in water, and, 
if the body were at rest, all that part of the body above A, 
would move in a direction opposite to that in which C is 
struck. For every point C, at which a body may be struck, 
or every center of percussion, there is a corresponding point 
A, on the other side of the center of the figure through 
which passes an axis of spontaneous rotation round which 
the body rotates ; i. e., if the lower part is suddenly pulled 
forward, the upper part above A, will move backward. 

e— The distance, A, C, is equal to ^ when the body 



26 



THE TOWER CLOCK 



is suspended at A, k being the radius of gyration 

k- 
in this case ; or, p^'- when suspended at C. k being the 

radius of gyration in this case. The radii of gyration are so 
k^ Jc| 
AB = CB 

^ Point of Suspension. 



related that 



B Center of Gravit J'. 



C Center of Oscilation. 



Fig. 19. Principal Points of a Simple Peiululuin. 

2 — The radius of oscillation is the distance of the center 
of oscillation from the point of suspension; see Fig. 19. 
and equals the square of the radius of gyration divided by 
the distance of the center of gravity from the point of sus- 
pension or axis. 

5 — The center of gyration with reference to an axis, is a 
point at which, if it were possible to collect the entire zveight 
of a body at one point, its moment of inertia will remain un- 
changed ; or, in a revolving body, the point at which the 
whole weight of the ])ody may be concentrated. The dis- 
tance of this point frdui llir axis or point of suspension is 
the radius of gvration. 

4 — The moment of inertia of the weigJtt of a body with 
respect to an axis, or point of suspension, is the algebraic 



How TO MAKE IT. 27 

sum of the products obtained by multiplying the weight of 
each elementary particle by the square of its distance from 
the axis, or point of suspension. If the moment of inertia 
with respect to an axis equal I, the weight of any element of 
the body equal w, and its distance from the axis equal r, we 
have I = S (wr''). 

The moment of inertia varies in the same body according 
to the position of the axis. It is the least possible when 
the axis passes through the center of gravity. To find the 
moment of inertia of the body referred to a given axis, 
divide the body into small parts of regular figure. 

Multiply the weight of each part by the square of the dis- 
tance of its center of gravity from the axis. The sum of the 
products is the moment of inertia. 

The value of the moment of inertia thus obtained will be 
more nearly exact, the smaller and more numerous the parts 
into which the body is divided. 

The moments of inertia of regular solids, the formulae for 
which apply to our problem, are as follows: 

a — Rod or bar of uniform thickness, with respect to an 
axis perpendicular to the length of the rod : 

I = W (T + d') 

W = weight of rod. 2I = length of rod. d = distance of 
center of gravity from the axis of suspension. 

b — Thin circular plate with its axis on its own plane : 

I = W(Ji +d') 
4 

r = radius of plate, 
c — Circular ring, axis perpendicular to its own plane : 

I = W ( ^''' ^ *"' + d'-') 
2 

R and r equals exterior and interior radii of the ring. 

The moment of inertia S wr^ numerically, equals the 
weight of a body, which, if concentrated at the distance 
unity from the axis of rotation, or suspension, would require 
the same work to produce a given increase in angular 
velocity that the actual body requires. 



28 THE TOWER CLOCK 

5 — The center and radius pi gyration. The center of gy- 
ration with reference to an axis of suspension, is a point at 
which, if the entire weight of a body be concentrated, its 
moment of inertia will remain unchanged. The distance of 
the point from the axis, or point of suspension, is the radius 
of gyration. 

If W equals the weight of a body, I equals ;? wr- or its 

moment of inertia, and k equals its radius of gyration. 
Then I = Wk^ = ^ wr'^ 



4 



That is : the moment of inertia equals the weight multiplied 
by the square of the radius of g>'ration. 

To find the radius of gyration, divide the body into a con- 
siderable number of small parts, the greater the number of 
parts, the more accurate the result, then take the mean of 
all the squares of the distances of the parts from the axis, or 
point of suspension, and find the square root of the mean 
square. Or, if the moment of inertia is known, divide it by 
the weight and extract the square root. 

The principal radii of gyration called for in the consider- 
ation of this pendulum are as follows : 

a. Rod, axis perpendicular to its length = k = i ^/ - — 

b. Circular plate axis in its own plane, = k = — 

2 

c. Circular ring, its axis perpendicular to the plane of the ring. 

/r^+7 

k 



= nI' 



2 

The value of k, and of the squares of the radii of gyration, 
for the above formulae are : 

Radius of gyration. Squares of the radii of gyration. 



•57731 — •' 



3 



b: .7071 



c. .7071 VK' + r^ (R* + 



HOW TO MAKE IT. 



29 



6 — Center of Percussion, of a body oscillating about a 
fixed axis, is the point at which, if a blow is struck by the 
body, the percussive action is the same as though the whole 
mass of the body were concentrated at that point ; see also 
paragraph No. c and d in the definition of centers of oscil- 
lation. The center of percussion is identical with the center 
of oscillation. All of us who are familiar with the use of 
the baseball bat will have some very vivid remembrances 
of the same percussive action. When the bat is struck above 
the center of percussion, do you remember how it made 
your fingers tingle, and when it hit too low down, how the 
bat went waltzing oil toward the field ? 



2 



3 

t 



4 



5 



6 

-4- 



r 



8 



\ ' 

; « 

I i 

I . I 



s 



^^ 




i';"."y.":'"j 



Fig. 20. Parts of pendulum as separated for calculating the weight. 



Fig. 20 shows in table form the subdivisions of the pend- 
ulum and the results of the application of the formulae, 
from which we get the following results : 



30 



THK TOWER CLOCK 



♦Squares of Radii 
of Gyration 


I 
.1 19140 


2 
.30664 


3 

I. 531 2 


4 

2.6562 


5 

1.422988 


tWeights of Paits 


1.2C6036 


.271625 


•939497 


6.480522 


.728 


Moments of Inertia 


.143686 


.083291 


r. 438562 


17.213504 


I 035944 


§Center of Oscill'n 


.0304 


.00784 


.03916 


.06970 


.03630 


*Squares of Radii 
of Gyration 


6 

I 137573 


7 
1. 125 


8 
3675 


Total. 


tWeights of Parts 


27.5COQ56 


2.5977'o 


.401 


40.125356 


Moments of Inertia 


31.285C23 


2.922412 


14.736750 


68859172 


§Centres of Oscil'n 


.02830 


.02870 


.93992 


1.17082 



*The sqtiare root of the mean square equals .9448, which, 
according to the formula, equals the distance from B to C, 
Fig. 19 by this formula. 

fThen, by the formula, we want the square root of 68.859 
divided by 40.125 (the weight) equals i. 31009, which is 
the distance between B and C, by this formula. 

§By the formula 1. 17082 is the distance from B to C. 

Now here are three different results by three formulae; 
theoretically they should agree, but I have not succeeded in 
finding any one who can make them do so ; I find also, that 
all the eminent authorities give as a final conclusion the fact 
that it is, after all, still a matter of experiment and trial ; scf 
I do not think we need to worry ourselves over the lack of a 
definite result. 

After all the calculations arc made, there still reinains 
the effect of barometric changes which are not included in 
the formulae given. 

Prof. vS. W. Stratton, of the U. S. Bureau of Standards 
at Washington, tells me of a new nickel steel alloy known 
by the name of "Invar," made in France by the Societe de 
Commentry-Fourchambault, d'Imphy. The coefficient of 
expansion of this alloy is practically zero, and is to be used 
in some of the new apparatus where it is desirable to elimi- 



HOW TO MAKE IT. 3 1 

nate temperature effects. This new metal will be the ideal 
material for pendulums. 

We will now go back to the \\ou\ shaft and proceed to- 
wards the dials. The pair of beveled gears of 44 and 48 
teeth, with their shafts at 90 degrees, are for leading off 
to the large dials, which should be above the clock. It is 
best to use the well-known universal joint, see Fig. 7, to 
connect the shaft which goes from this pair of gears to the 
nest of gears. Fig. 8, which will run the hands on the four 
dials ; and as the four gears receiving the impulse from the 
hour shaft must have the same speed as the hour shaft, they 
must all have the same diameter, and the one on the vertical 
shaft in the center must be enough larger in diameter to run 
the hour gears without their interference with each other. 
The number of teeth in the gears of the nest of four is 44, 
and the driving wheel is 48, giving center angles of 42 
degrees 30 minutes for the 44 toothed wheel, and 47 degrees 
30 minutes for the 48-toothed wheel. The universal-jointed 
shafts from the clock to the nest of gears, and those from 
this nest of gears to the back of the dials must have the 
slip, or expansion joint, shown in Fig. 7, to allow for all 
expansion caused by changes in the weather, wind pressure 
on the dials, etc. 

The shafts to the dials will, of course, revolve once an 
hour, and so these shafts carrv the minute hands. To obtain 
the motion of the hour hand the usual combinations of 
wheels of 96 teeth and pinions of 24 teeth, driving wheels 
of 90 teeth and pinions of 30 teeth, are used behind each 
dial, to obtain one revolution in 12 hours. Of course, any 
other combination would do equally well, so long as it satis- 



W W 



= 12 



fies the condition of the following equation : pp, 

Wequals teeth in the wheels; V equals those in the pinion. 

In case the hour shaft of the clock is not perpendicularly 
under the nest of gears above, care must be taken that a 
short section of the universal-jointed shaft at each end is 



HOW TO MAKE IT. 



33 




34 



THF TOWER CLOCK 



■^g^'^^'^^^^^^^ 



t^ian 



F-ft* 



■il ^S!;v^\x.■'■>x-^;^;^?;^ 




l.l 



wW 



Fig. 17. Arrangement of Hands, Counter Balances and Hour and Minute 
Wheels at the Centers of the Clock Dials. 



now TO MAKE IT. 



35 



exactly perpendicular, in order to avoid the loss of motion, 
and therefore of reg-tilarity of time, which will occur if the 
angles of obliquity are not equal. 

The hands are made of copper, elliptical in section, being 
made up of two circular segments brazed together at the 
edges, with internal diaphragms to stiffen them. The min- 
ute hand is straight and perfectly plain, with a blunt point. 

At the center of the dial the width of the minute hand is 
one-thirteenth of its length, tapering to about half as much 
at the point. 

The hour hand is about the same width, ending just short 
of the dial figure and terminating in a palm or ornament. 
The external counterpoises are one-third the length of the 
minute hand, and of such a shape that they will not be con- 
founded with either of the hands ; a cylinder, painted the 
same color as the dial, makes a good counterpoise. This 
counterpoise may be partly on the inside of the dial if it 
is desired to keep it invisible, but it should not be omitted, 
as it saves a good deal of power, prevents the twisting of 
the arbors, and also assists in overcoming the action of 
the wind on the hands. Two-thirds of the counterpoise 
weight may be inside. 

The diameter of the dials and the weight of the bells are 
the two most important factors in the design of a clock. 

This clock was designed, as the specifications show, for 
four dials of 12 feet diameter and an hour bell of 7,000 
pounds. As it is not yet known in what tower the University 
will set the clock, and therefore the height of the dials 
above the ground, the mechanical parts are designed for a 
15 foot dial. 

The diameter of the dials should not be less than one- 
tenth of their height above the ground, so the limit of 
height for a 15-foot dial should be 150 feet. 

The figures and minutes together will take up one-third 
of the radius of the dial; the figures two-thirds of this, 
or two-ninths of the radius, and the minutes two-thirds of 



36 THE TOWER CLOCK 

the remaining one-ninth of the radius, with every fifth min- 
ute more strongly marked than the rest. 

How many of . the thousands of people who pass daily 
up and down Michigan avenue, do you suppose have ever 
noticed, or if they have noticed it once, have ever thought 
of it again, that the clock face on the Kimball Company's 
tower has the name of the company instead of the numbers, 
to indicate the hours? In several towns in New England 
I have seen the words Memorial Gift distributed round the 
dial, and in one case the name of the giver was used for the 
same purpose. In Toronto, Canada, I passed the big 22 
foot dial on the City Hall clock fully 25 times before I 
noticed that there were no figures or letters of any kind but 
only 12 broad flat surfaces about the width of the figure 
three of the Roman numerals, as used on clock dials, and 
I find that Sir Edmund Beckett specially recommends the 
last form for illuminated dials, as there can be a greater 
area of lighted surface in the figure ring, which will add 
to the facility in reading the time. If you will stop to 
think, you will see at once that it is never the Hgnres that 
you read, but the angles of the minute and hour hands in 
their relation to each other and to the 12 sub-divisions of 
the dial ; therefore on this clock the hours will be indicated 
by heavy bars or bands, about five inches wide, instead of 
by the numerals. 

The dial proper will be illuminated and is therefore built 
up in segments ; the outer series containing the minutes and 
hours, in six segments; the inner series of four segments 
making up the center of the dial. 

The frame is of cast-iron, made in such sections that the 
opal glass, of about 22 ounces per square foot, can be set 
in it, as in ordinary sash, the segments being made to fit 
together with the lap or tongue and groove joints, so as to 
exclude the rain and snow. 

The hands and figures will be painted black, and the 
frame work of the dial gilded. A space of about three feet 



HOW-TO MAKE IT. 37 

at the back of 'each dial will be enclosed and this wall will 
be used to support the illuminating medium, which in this 
case will probably be about 60 incandescent lamps to each 
dial, with powerful reflectors that will distribute their light 
as evenly as possible over the whole surface of the dial. 



THE STRIKING TRAIN. 

.■ As the striking part should be wound up every 24 hours, 
with an allowance of six hours extra for carelessness about 
the time of winding, provision must be made for 30 hours' 
work. There are 156 strokes in 24 hours, and allowing 60 
strokes extra for overtime, makes 216 strokes to provide for. 

The train is arranged to allow the second wheel. No. 32, 
one revolution for each stroke on the bell. The cam. No. 
27, on the going shaft has 12 parts, therefore it will have 
one-twelfth revolution to each stroke. 

If we allow 18 teeth on the pinion. No. 31, on the second 
shaft, No. 30, the great wheel. No. 29, will have 216 teeth, 
or one revolution for every 12 strokes, which gives 18 turns 
in 30 hours. The length of the winding barrel, No. 26, 
must of course, provide for this. 

The bell, of 7,000 pounds, calls for a striking weight of 
one-fiftieth of its weight, or 140 pounds. The levers, Nos. 
28 and 28', are in the proportion of one to three, giving a 
pressure on the cam surfaces, No. 27, of 420 pounds, and 
adding one-tenth for friction, makes it equal to 480, or for 
safety, 500 pounds pressure on the cams, which are of cast- 
steel. The end of the lever. No. 28, has a hardened steel 
shoe to reduce the friction to its lowest point. 

The second wheel, No. 32, has 120 teeth, with a pinion 
of 20 teeth. No. 33, on the third shaft, giving six revolu- 
tions of the fly shaft and therefore of the fly. 

The details of the fly and its clutch are shown in Fig. 10. 
The vanes are so made that they may be set to present any 
desired amount of surface to the air. This gives us an 
opportunity to determine definitely the striking periods, 

(38) 



HOW TO MAKE IT. 



39 




40 THE TOWER CLOCK 

* 

which on a bell of 7,000 pounds should be very slow, as it 
requires two or two and one-half seconds for each stroke in 
order to obtain the full vibration of the bell. 

The fly clutch is the familiar roller clutch, and is made 
with a set of eight steel cylinders, C, rolling in angular 
spaces, B. As the shaft starts to revolve, one or more of 
these rollers is always in position to roll into the angle 
between the ratchet wheel, B, and its case, D, and so start 
the vanes. As the shaft stops its revolution, the vanes, G, 
and the case, D, are free to revolve, so that, by their mo- 
mentum they roll the cylinders out of the acute angles and 
into the right angled spaces, which are large enough to 
hold the rollers free of all moving parts. 

The locking plate. No. 39, Fig. i, is carried forward by 
a wheel, No. 38, of 78 teeth, which equals the number of 
strokes in 12 hours. This is moved one tooth for each 
stroke, by the pinion. No. 37, of 12 teeth, on the going 
shaft. No. 25. 

The going shaft has a winding gear of 96 teeth, with a 
pinion on the winding shaft of 24 teeth. This pinion slides 
on a feather so that it can be thrown out of gear after 
winding, in order to save power. 

Fig. II shows the positions, in full lines, of the various 
parts of the locking plate work of the striking side at seven 
and one-half minutes of the striking of the hour, except 
the cam or snail, j, which is shown at the instant after the 
striking begins. The total angular movement of the hour 
pin from the point of first contact to the warning is 22^/2 
degrees. 

The movement is as follows : The hour pin, a, in wheel 
No. 9, moving in the direction of the arrow, begins to de- 
press the lever, b, on the shaft, c, this raises the levers, d 
and e. The lever, d, carries the roller, d', and e, carries 
the pin, e'. The pin, f, drops into notches, h, on the lock- 
ing plate. No. 39. After an angular movement of 22^/^ 
degrees, the hour pin has raised the roller, d', and the pin, 



HOW TO MAKE IT. 



41 




42 THE TOWER CLOCK 

e', to d" e", when the pin, m', will pass at five minutes of the 
hour, allowing the fly to revolve 240 degrees, giving the 
warning and revolving the cam, o, 223/2 degrees, or far 
enough for the roller, d', to rest on its circumference, there- 
by preventing f, from dropping back into the notch, h. As 
the pin, m', passes, n', will come in contact with the pin, 
g', in the lever, g. The lever, g, receives its impulse from 
the snail or cam, j, on the wheel. No. 10, which revolves 
once in 15 minutes. The cam is so designed that the pin, 
g', comes up into position six minutes before the hour, and 
so catches pin, n', as it comes along at five minutes of the 
hour. The pin, i', drops a sufficient interval before the 
hour (about three seconds), for the striking mechanism to 
get in motion so as to give the first blow of the hour ex- 
actly on the first second of the hour. The set screws shown 
at K, allow an angular movement of five seconds either way 
to give the required adjustment. 

After the pin, g', has released n', of course the fly revolves 
until the required number of strokes have been given; the 
pin, f, dropping upon the locking plate for each blow, until 
one of the notches comes under it, when, f, drops into it, 
letting the roller, d', drop into the hollow in the cam, o, and 
the lever, e, drop, so that the pin, e', catches m', when all 
movement ceases except the fly, which, released by the 
clutch, continues to revolve until its momentum has been 
overcome. 

Of course the movements of the snail, j, and of the parts 
that work with it are repeated every 15 minutes; but as the 
pin, n', is not in position, there is no movement of the rest 
of the hour-striking train. 

The train must be so adjusted that after striking the 
hour the hammer shall be left at the top of its lift, and 
ready for the next blow, though I think it would be better 
to leave it at about three-quarters lift, so that there would 
be less strain on the points of the faces of the cams of the 
hour-striking wheel. The cam faces of this wheel are gen- 
crated in the same manner as for the chime side, see Fig. 13. 



HOW TO MAKE IT. 



43 



5= 






m 






=5E 



^'^ 



^!^; 



>?, 



=5^ 



op 



i^lii 



5E 






^ 



THE CHIME TRAIN. 

The Westminster Chime, so-called, which is a copy of 
the chime of St. Mary's at Cambridge, England, and which 
originated over loo years ago, has been adopted for the 
quarters in this clock. The notes are E, D, C, and G ; or, 
as arranged by the Meneely Company ; F on a bell of 2,079 
pounds; B flat 875 pounds; C, 616 pounds; D, 437 pounds, 
and] with the hour bell to give the note B flat an octave 
below. If we give the numbers 6, 3, 2, i, to the chime, the 
arrangement of the chime is as follows : 



Second Quarter j 3;>26 1 



,^A r fourth Quarter 
V 1326 [ ■^ 

Third Quarter j 6213 ) 

( I2j6 y First Quarter 

If you study this table carefully, you will see that the 
chimes are repeated twice in an hour. The cams are ar- 
ranged to turn once every hour. 

The interval between the sets of strokes is of considerable 
importance, in order to enable the listener to read the quar- 
ters correctly. Taking the interval between the strokes of 
each set of four strokes as a standard, Sir Edmund Beckett 
found that two and one-half spaces or intervals between 
the sets of four strokes gave the best result. Now to avoid 
the fractions, and calling the spaces two, then there will 
be five spaces between sets, or 55 spaces, and as the chime 
is repeated twice in the hour, this would give no spaces 
on the cam surfaces for each hour. The chime laid out 
graphically would look like Fig. 12, which explains itself. 
As F is struck by two cams, it has been given two lines. 

Allowing two teeth on the great wheel. No. 54, for each 
space will make 220 teeth on the great wheel, which, with 
a pinion, No. 55, of 22 teeth, gives 10 revolutions of the 
second shaft, No, 56, and one revolution to each set of 

(44) 



HOW TO MAKE IT. 



45 



four strokes in the chime. On the second shaft is a wheel, 
No. 57, of 1 20 teeth, driving a pinion, No. 58, of 20 teeth 
on the fly shaft, thus giving six revokttions to each set of 
four strokes in the chime. The fly ckitch and other parts 
are the same as in the striking side. There are five cams ; 
the first will strike all of the No. i bells at the proper inter- 
vals ; the second all of the No. 2 bells ; the third all of the 
No. 3 bells, while the fourth and fifth will divide the nunv 
ber six strokes between them. This is necessary because 
there are two periods when the No. 6 bells come so near 
together that it would be impossible to get the levers raised 
in time for the second stroke. 

The striking weights on these bells increase from one- 
sixtieth to one-fortieth of the weight of the bells, from the 
large to the small ones, so that F, bell will have a striking 
weight of 35 pounds; B flat, of 18 pounds; C, of 12 pound-: 
and D, of 11 pounds. As there are twO' F hammers, the 
total weight of the hammers is iii pounds. Of course we 
can make the pressure on the cam surfaces anything we 
please, by altering the relative length of the arms of the 
respective levers. There cannot be more than three of the 
six levers on the cams at the same time, as you will observe 
by referring to the assembled drawing, Fig. i, so that the 
greatest possible weight would be that covered by raising 
the three largest hammers, or 88 pounds. 

The parts have been proportioned to use, as nearly as 
possible, the same driving power as on the striking side. 

The main driving shaft also carries the locking plate, t', 
divided properly for the four quarters. 

In the locking plate work of the chime side, the wheel. 
No. 9, Fig. 14, on the hour shaft of the time train carries 
the pins a\ a", a^ a*, which depresses lever, b, and raises 
levers, c, d, and e, allowing the pin, m', to pass c', raising 
e, out of slot e', in the locking plate, t', and the roller, d', 
out of the cam, o, allowing the fly and the three armed 
lever, k, 1, m, to revolve 240 degrees, when the pin, 1', is 



46 



THE TOWER CLOCK 




HOW TO MAKE IT. 



47 



caught by pin, W, on the lever, h, which has, in the mean- 
time, been raised up to. its position by the pin, g', in the 
lever, g, riding- on the cam surfaces, f\ f^, f^, f*, on the 
rim of the wheel, No. 9. 

The pin, g', drops from these cams allowing pin, 1', to 
pass, when the ringing of the quarters proceeds, and closes, 
the same as in the striking of the hours. 

The cams, f, are faced with hardened steel, and f\ f^ and 
f^, are set so that they will discharge the quarters at such 
an interval before the end of the quarter, that they will 
strike the first blow on the first second of the next quarter, 
f*, is made to drop the pin, g', at such a period before the 
end of the hour that the interval between the last stroke 
of the fourth quarter chime will be one second more than 
that between the parts of the chime. If you will refer to 
the graphic form of the chime, Fig. 12, you will see that 
the interval between the sets of four strokes is five, and the 
interval between strokes is two. Allowing two seconds be- 
tween strokes of the chime, to obtain the full volume of 
sound, five seconds between sets, and six seconds at the 
end, we shall have 45 seconds of time, or an angular move- 
ment of four and five-tenths degrees ahead of the quarters. 
In order to obtain exact time at this point the cam face 
f* is made adjustable. 

A cam as used here is a tooth which is to raise a lever to 
its limit without assistance, while a tooth in a wheel would 
be assisted by the one behind it ; and as the greatest strain 
comes when the cam is getting the lever started from a 
standstill, the cam must be so formed as to begin the lift at 
the end of the lever where the greatest power is required, 
and the extreme end of the lever must be carried up to the 
exact moment of dropping, and then let drop suddenly at 
that exact moment. 

Of course the theoretical curve of the cam surfaces should 
be the epicycloid ; but this construction by means of arcs of 
circles is just as good in actual practice, if designed for 



HOW TO MAKE IT. 49 

each cam separately. By reference to Fig. 13, C, A, L, is the 
line of centers; L, the lever center; A, is the pitch circle 
of the cam ; A', B, is the pitch distance, which equals A B, 
plus one-eighth, for clearance as the lever drops, so that it 
will not strike the cam below. A, P, is the arc of the lever. 
Draw A, T, tangent to the pitch circle at A, and B, T, tan- 
gent to the pitch circle at B. From P, draw a tangent to 
the lever arc, and the intersection of these three tangents 
will be the center of an arc of a circle which will be the 
proper curve for the cam surface, to carry the end of the 
lever at the beginning and end of its service. The cams 
must be backed off for clearance as the lever falls. 



THE SHAPES AND WEIGHTS OF BELLS. 

Of course we are not concerned with the bells that are 
to be used with this clock, as they are to be supplied by 
the University. But the fact remains that, as the size of 
the clock depends, for one of its factors, upon the size of 
the bell, it will be necessary for us to know something of 
the proper proportions and method of obtaining the full 
vibration and tone, from any given bell, or series of bells. 
The theory of the design of bells to produce a given series 
of notes, is based upon the law, that the number of vibra- 
tions in a second, in similar bells — that is, bells whose vari- 
ations in proportion are alike — varies as the square of the 
thickness, divided by the diameter; or, the depth of the 
notes, or the time of vibration varies as the diameter, 
divided by the square of the thickness. So' if we wanted to 
make a set of bells of the same thickness, not proportion- 
ate thickness, their other dimension must be as the square 
roots of a set of numbers in the inverse ratio of the vibra- 
tions belonging to the proposed notes. But if the thickness 
itself varies as the diameter, the sizes will vary simply as 
those numbers vary ; and therefore, all of the dimensions of 

a peal of eight bells will be in the proportions : 

T 8 4 .s 2 .■? 1 

■^' 7' fi' T' 5^' -, ' ' -" 

or, 6o", 53 1-3", 48", 45", 40", 3^", 32", 30". 

This being the diameter in inches of a peal of eight bells 

in the key of D flat. 

The weights of similar bells vary as the cubes of their 
diameters ; therefore the weights of a peal of eight bells 
would be, with the tenor weighing 100 for facility of com- 
parison : 

(50) 



HOW TO MAKE IT. 5I 

100, —70.23, —51.2, —42.2, —29.63, —21.6, —15.18, —12.5 
But the question at once arises, what is the proper weight 
for a given note or a given size? Taking 6 feet diameter 
as a convenient standard, the least weight for a bell of 72 
inches would be 8,064 pounds. Such a bell will be very 
near B flat according to the universal pitch, in which A 
has 880 vibrations per second, or, that number multiplied 
or divided by some power of 2. The diameter of bells on 
that scale is about 13 times the thickness of the sound bow. 
The sound bow should not be thinner than this, for there 
is a fullness and softness about a thick bell which a thin one 
can never have, and this loss of tone is even greater now, 
than it was a hundred years ago on account of the quality of 
the copper used in the bell. 

The modern process of smelting gives copper that is less 
tough and will hold less tin without becoming brittle, as 
well as being apparently incapable of a certain softness of 
tone which the old bells sometimes have, and which is very 
seldom secured in the modern ones. 

Sir Edmund Beckett says : "After trying and observing 
the effect of a great many patterns, and without favoring 
any particular curve, the one which gave the best effect was 
very like the ellipse in section, though not the same ellipse 
that was and still is, used by some of the English bell found- 
ers. And after further experiments with slightly varying 
shapes, I came to the conclusion that the following is the 
best shape for large bells on the 13 scale of thickness." — See 

Fig. 15- 

Divide the diameter of the bell mouth into 24 equal parts. 
Then the inside curve is the quarter of an ellipse whose ma- 
jor semi-axis A, C, is 14 parts of the diameter, and the 
minor semi-axis B, C, is 6 parts of the diameter. 

The outside curve cannot, of course, be a single curve, 
but must be an empirical curve made in such a way that it 
will give what has been found to be the best proportions for 
thickness throughout. As the thickness of the waist of the 



52 



TTfE TOWER CLOCK 




FiK. 15- Method of desiijnitiy hells. 



HOAV TO MAKE IT. ^^ 

bell, is to be one-third of the sound bow P, Q, which is one- 
thirteenth of the diameter b, must be one-thirty-ninth or 
two-thirds of a "part" outside of B. It is necessary to put the 
minor axis c b, one-half "part" belQw C B, in order to make 
the curve come right at the mouth of the bell, c b, and c a, 
are the semi-axes of the outer curve, the lower part, a R, is 
useless and the remaining- curve is made up as follows : 
Draw s Q P 4, to the point 4, in the base line, and make P 
Q, one-thirteenth of the diameter of the bell ; with radius of 
3>^ or 4 "parts", draw the arc A Q, the curve Q R, is any 
convenient tangent curve. The top is drawn as a circular 
arc varying from 16^ to 18 "parts", with E, as a center, the 
connecting part between the top and the waist is a cylinder. 

The composition recommended for the metal is 13 parts 
copper to 4 parts of tin, by weight, which would be written 
as a chemical compound: (Cug Sng.) 

Another formula for the curves of bells which gives a 
taller and thinner bell but of practically the same weight for 
similar diameters, and thickness at the sound-bow, is as fol- 
lows: Make the line, f a, Fig. 16 equal to the desired diam- 
eter, and the center line, C C, perpendicular to f a. Divide 
f a, into 10 equal parts. Parallel to the center line C C, 
draw the line, b, making the distance from b, to C, equal to 
2^ "parts" so that the diameter of the "waist" of the bell is 
one-half that of the mouth. From a, as center, and with a 
radius of eight "parts" describe an arc cutting the line, b, at 
the point 8 ; draw the line, a 8, and divide it into eight "parts" 
I, 2, 3, etc. Through these points draw the ordinates per- 
pendicular to, a 8, and make them equal to the length given 

in the following table : 

part. 



Length of 


ordinate through point 

44 II 41 


I - 

2 


0.41 
0.86 




(4 If If 


3 


1.02 




•4 14 (1 


4 = 


1,00 




4< 44 14 


5 =- 

6 = 


0.87 
0.66 




ii 44 44 
41 (( tl 


7 ^ 

8 = 


0.39 
0.09 



54 



THE TOWER CLOCK 



frfn fTTT] ro 




Fiy. i6. Second MK'thocl of desiytiintr bolls. 



HOW TO MAKE IT. 55 

These distances locate the centers of circles whose diame- 
ters are based upon the desired thickness of the bell at the 
sound bow. If the same scale of thickness used in the first 
formula is adhered to, viz : t=one-thirteenth of the diam- 
eter of the bell at its mouth then the diameter of the circle, 
d, on ordinate, 1, will equal one-thirteenth of the line, f a, 
and with the diameter of d, as a scale make the diameters of 
the circles on the other ordinates according to the following 
table : 

Diameter of circle on ordinate i = d 

2 = 0.653 " 

3 = 0.4; 4 " 
" " " " •• 4 = 380 " 
<• u it tt it j> ___ ^ iiy ** 

" " 6 = 0.291 " 

" " 7 = 0.279 " 

8 = 0.267 " 

Draw a curve tangent to these circles and finish the curve 
from d, to a, in a similar way to that given in the preceding 
formula. The curve of the crown may also be found in the 
same way. 

No provision is made for a tongue as bells intended for 
service with a clock should not be rung. 

Two forms of crowns are shown. 

Fig. 17 shows the detail of the dial, dial gears, universal 
joint and expansion joint, together with the inside counter 
weight for the minute hand. This counter balance should 
be a small weight on a long arm, rather than a heavy weight 
on a short arm, for, the nearer the length of the arm carry- 
ing the weight approaches that of the minute hand, the 
more perfect the balance. 

To balance the minute hand, it should be mounted upon 
its arbor, together with the counter-weight arm and tested 
on the balancing-ways, shifting the counter-weight until a 
perfect balance is obtained ; mark the position of the weight 
on its lever, then when these parts are assembled you are 
sure the balance is perfect. 

^ cfc. 



56 



THE TOWER CEOCK 




Fig. 18. Sectional view of clock and bells. 

L.ofC. 



HOW TO MAKE IT. 57 

Before using the balancing ways, see that the longitudinal 
and transverse spirit levels show the bubble in the center ; if 
they do not, set the adjusting screws up or down until you 
have a perfectly level table. 

The visible counter weights of the hour and minute hands 
are of copper, together with the hands so that they can be 
brazed together securely, and also, because copper is the 
only thing that will not corrode badly under exposure to the 
weather. 

Just a word in closing in regard to towers : It is quite im- 
portant that it should be known before the architect designs 
the tower for a building whether a clock and bells are to be 
placed in it or not. The clock room and therefore the dials 
should be below the bells, for greater stability; and large 
enough to give space in which to enclose the clock by itself, 
and still leave room to inspect it from all sides. 

The bell chamber should be as large as it is possible to 
make it, as the bells always sound better. Another import- 
ant point is the windows ; in a good many cases, the full tone 
and vibration of the bell cannot be obtained because the bell 
is hung too low. They must at least be hung above the sills 
of the windows. Louvres or overlapping boards to keep out 
the rain are another source of failure to get the best results 
from a bell. 



PRACTICAL BOOKS 

FOR 

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PUBLISHED BY 

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rav 29 1903 

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■•?*;; 



LIBRARY OF CONGRESS 

Hi 
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